205:
2418:(United States). The specific rolling resistance in bearings varies with both wheel loading and speed. Wheel bearing rolling resistance is lowest with high axle loads and intermediate speeds of 60–80 km/h with a Crr of 0.00013 (axle load of 21 tonnes). For empty freight cars with axle loads of 5.5 tonnes, Crr goes up to 0.00020 at 60 km/h but at a low speed of 20 km/h it increases to 0.00024 and at a high speed (for freight trains) of 120 km/h it is 0.00028. The Crr obtained above is added to the Crr of the other components to obtain the total Crr for the wheels.
235:
contact area at the right side, travels through the contact patch and leaves at the left side. Initially its vertical deformation is increasing, which is resisted by the hysteresis effect. Therefore, an additional pressure is generated to avoid interpenetration of the two surfaces. Later its vertical deformation is decreasing. This is again resisted by the hysteresis effect. In this case this decreases the pressure that is needed to keep the two bodies separate.
2120:
notable that slip does not occur in driven wheels, which are not subjected to driving torque, under different conditions except braking. Therefore, rolling resistance, namely hysteresis loss, is the main source of energy dissipation in driven wheels or axles, whereas in the drive wheels and axles slip resistance, namely loss due to wheel slip, plays the role as well as rolling resistance. Significance of rolling or slip resistance is largely dependent on the
1912:
carriage wheels. But there are other tests on carriage wheels that do not agree. Theory of a cylinder rolling on an elastic roadway also gives this same rule These contradict earlier (1785) tests by
Coulomb of rolling wooden cylinders where Coulomb reported that rolling resistance was inversely proportional to the diameter of the wheel (known as "Coulomb's law"). This disputed (or wrongly applied) -"Coulomb's law" is still found in handbooks, however.
2144:). Such torques results in energy dissipation (above that due to the basic rolling resistance of a freely rolling, i.e. except slip resistance). This additional loss is in part due to the fact that there is some slipping of the wheel, and for pneumatic tires, there is more flexing of the sidewalls due to the torque. Slip is defined such that a 2% slip means that the circumferential speed of the driving wheel exceeds the speed of the vehicle by 2%.
287:
includes wheel bearing resistance, energy loss by shaking both the roadbed (and the earth underneath) and the vehicle itself, and by sliding of the wheel, road/rail contact. Railroad textbooks seem to cover all these resistance forces but do not call their sum "rolling resistance" (broad sense) as is done in this article. They just sum up all the resistance forces (including aerodynamic drag) and call the sum basic train resistance (or the like).
4477:
663:. Thus, they are all just measures of resistance per unit vehicle weight. While they are all "specific resistances", sometimes they are just called "resistance" although they are really a coefficient (ratio)or a multiple thereof. If using pounds or kilograms as force units, mass is equal to weight (in earth's gravity a kilogram a mass weighs a kilogram and exerts a kilogram of force) so one could claim that
4467:
3079:, smaller wheels appeared to have similar or lower losses than large wheels, but these tests were done rolling the wheels against a small-diameter drum, which would theoretically remove the advantage of large-diameter wheels, thus making the tests irrelevant for resolving this issue. Another counter example to the claim of smaller wheels having higher rolling resistance can be found in the area of
2156:= force x velocity so that power per unit of velocity is just force). So just a small percentage increase in circumferential velocity due to slip can translate into a loss of traction power which may even exceed the power loss due to basic (ordinary) rolling resistance. For railroads, this effect may be even more pronounced due to the low rolling resistance of steel wheels.
862:) are usually performed on new tires. When measured by using these standard test practices, most new passenger tires have reported RRCs ranging from 0.007 to 0.014." In the case of bicycle tires, values of 0.0025 to 0.005 are achieved. These coefficients are measured on rollers, with power meters on road surfaces, or with
3837:, January 1970, pp. 83–88 (one article split between two journals) Except for the "Historical Introduction" and a survey of the literature, it is mainly about laboratory testing of mine railroad cast iron wheels of diameters 8″ to 24 done in the 1920s (almost a half century delay between experiment and publication).
272:
In other words, the vehicle would be coasting if it were not for the force to maintain constant speed. This broad sense includes wheel bearing resistance, the energy dissipated by vibration and oscillation of both the roadbed and the vehicle, and sliding of the wheel on the roadbed surface (pavement or a rail).
2230:
decreases Crr by 3%. But, if the inflation pressure is not changed, then a 20% increase in load results in a 4% increase in Crr. Of course, this will increase the rolling resistance by 20% due to the increase in load plus 1.2 x 4% due to the increase in Crr resulting in a 24.8% increase in rolling resistance.
2438:, which weighs 715 tonnes and carries 1323 passengers, resulting in a per-passenger weight of about half a tonne. This lighter weight per passenger, combined with the lower rolling resistance of steel wheels on steel rail means that an N700 Shinkansen is much more energy efficient than a typical automobile.
2190:. An exception is if the tractive effort is so high that the wheel is close to substantial slipping (more than just a few percent as discussed above), then slip rapidly increases with tractive effort and is no longer linear. With a little higher applied tractive effort the wheel spins out of control and the
3797:
Statistics of railroads of class I in the United States, Years 1965 to 1975: Statistical summary. Washington DC, Association of
American Railroads, Economics and Finance Dept. See table for Amtrak, p.16. To get the tons per passenger divide ton-miles (including locomotives) by passenger-miles. To get
1911:
According to Dupuit (1837), rolling resistance (of wheeled carriages with wooden wheels with iron tires) is approximately inversely proportional to the square root of wheel diameter. This rule has been experimentally verified for cast iron wheels (8″ - 24″ diameter) on steel rail and for 19th century
629:
is often multiplied by 1000 to get the parts per thousand, which is the same as kilograms (kg force) per metric ton (tonne = 1000 kg ), which is the same as pounds of resistance per 1000 pounds of load or
Newtons/kilo-Newton, etc. For the US railroads, lb/ton has been traditionally used; this is
290:
Since railroad rolling resistance in the broad sense may be a few times larger than just the pure rolling resistance reported values may be in serious conflict since they may be based on different definitions of "rolling resistance". The train's engines must, of course, provide the energy to overcome
2217:
The rolling resistance coefficient, Crr, significantly decreases as the weight of the rail car per wheel increases. For example, an empty freight car had about twice the Crr as a loaded car (Crr=0.002 vs. Crr=0.001). This same "economy of scale" shows up in testing of mine rail cars. The theoretical
2203:
Rolling resistance greatly increases with applied torque. At high torques, which apply a tangential force to the road of about half the weight of the vehicle, the rolling resistance may triple (a 200% increase). This is in part due to a slip of about 5%. The rolling resistance increase with applied
271:
In the broad sense, specific "rolling resistance" (for vehicles) is the force per unit vehicle weight required to move the vehicle on level ground at a constant slow speed where aerodynamic drag (air resistance) is insignificant and also where there are no traction (motor) forces or brakes applied.
220:
A characteristic of a deformable material such that the energy of deformation is greater than the energy of recovery. The rubber compound in a tire exhibits hysteresis. As the tire rotates under the weight of the vehicle, it experiences repeated cycles of deformation and recovery, and it dissipates
2376:
Temperature: with both solid and pneumatic tires, rolling resistance has been found to decrease as temperature increases (within a range of temperatures: i.e. there is an upper limit to this effect) For a rise in temperature from 30 °C to 70 °C the rolling resistance decreased by 20-25%.
2426:
The rolling resistance of steel wheels on steel rail of a train is far less than that of the rubber tires wheels of an automobile or truck. The weight of trains varies greatly; in some cases they may be much heavier per passenger or per net ton of freight than an automobile or truck, but in other
2354:
Sidewall deflection is not a direct measurement of rolling friction. A high quality tire with a high quality (and supple) casing will allow for more flex per energy loss than a cheap tire with a stiff sidewall. Again, on a bicycle, a quality tire with a supple casing will still roll easier than a
234:
This main principle is illustrated in the figure of the rolling cylinders. If two equal cylinders are pressed together then the contact surface is flat. In the absence of surface friction, contact stresses are normal (i.e. perpendicular) to the contact surface. Consider a particle that enters the
2754:
If one were to assume that the resistance coefficients (Crr) for motor vehicles were the same as for trains, then for trains the neglected resistances taken together have a Crr of about 0.0004 (see Астахов, Fig. 4.14, p.107 at 20km/hr and assume a total Crr =0.0010 based on Fig. 3.8, p.50 (plain
286:
The pure "rolling resistance" for a train is that which happens due to deformation and possible minor sliding at the wheel-road contact. For a rubber tire, an analogous energy loss happens over the entire tire, but it is still called "rolling resistance". In the broad sense, "rolling resistance"
122:
between the wheel and the surface also results in energy dissipation. Although some researchers have included this term in rolling resistance, some suggest that this dissipation term should be treated separately from rolling resistance because it is due to the applied torque to the wheel and the
2430:
As an example of a very heavy passenger train, in 1975, Amtrak passenger trains weighed a little over 7 tonnes per passenger, which is much heavier than an average of a little over one ton per passenger for an automobile. This means that for an Amtrak passenger train in 1975, much of the energy
2328:
Material - different fillers and polymers in tire composition can improve traction while reducing hysteresis. The replacement of some carbon black with higher-priced silica–silane is one common way of reducing rolling resistance. The use of exotic materials including nano-clay has been shown to
2119:
is usually not equal to the radius of the rolling body as a result of wheel slip. The slip between wheel and ground inevitably occurs whenever a driving or braking torque is applied to the wheel. Consequently, the linear speed of the vehicle differs from the wheel`s circumferential speed. It is
294:
For tires, rolling resistance is defined as the energy consumed by a tire per unit distance covered. It is also called rolling friction or rolling drag. It is one of the forces that act to oppose the motion of a driver. The main reason for this is that when the tires are in motion and touch the
2229:
For pneumatic tires, the direction of change in Crr (rolling resistance coefficient) depends on whether or not tire inflation is increased with increasing load. It is reported that, if inflation pressure is increased with load according to an (undefined) "schedule", then a 20% increase in load
2441:
In the case of freight, CSX ran an advertisement campaign in 2013 claiming that their freight trains move "a ton of freight 436 miles on a gallon of fuel", whereas some sources claim trucks move a ton of freight about 130 miles per gallon of fuel, indicating trains are more efficient overall.
3083:
soap box derby racing. In this race, the speeds have increased as wheel diameters have decreased by up to 50%. This might suggest that rolling resistance may not be increasing significantly with smaller diameter within a practical range, if any other of the many variables involved have been
2355:
cheap tire with a stiff casing. Similarly, as noted by
Goodyear truck tires, a tire with a "fuel saving" casing will benefit the fuel economy through many tread lives (i.e. retreading), while a tire with a "fuel saving" tread design will only benefit until the tread wears down.
3017:
Baker, Ira O., "Treatise on roads and pavements". New York, John Wiley, 1914. Stagecoach: Table 7, p. 28. Diameter: pp. 22-23. This book reports a few hundred values of rolling resistance for various animal-powered vehicles under various condition, mostly from 19th century
2312:
as a by-product. The sound generated by automobile and truck tires as they roll (especially noticeable at highway speeds) is mostly due to the percussion of the tire treads, and compression (and subsequent decompression) of air temporarily captured within the treads.
2362:
thickness and shape has much to do with rolling resistance. The thicker and more contoured the tread, the higher the rolling resistance Thus, the "fastest" bicycle tires have very little tread and heavy duty trucks get the best fuel economy as the tire tread wears
2755:
bearings) and adjust for roller bearings based on a delta Crr of 0.00035 as read from Figs. 4.2 and 4.4 on pp. 74, 76). Compare this Crr of 0.0004 to motor vehicle tire Crr's of at least 10 times higher per "Rolling resistance coefficient examples" in this article
2350:
Over inflating tires (such a bicycle tires) may not lower the overall rolling resistance as the tire may skip and hop over the road surface. Traction is sacrificed, and overall rolling friction may not be reduced as the wheel rotational speed changes and slippage
31:
2339:
Extent of inflation - Lower pressure in tires results in more flexing of the sidewalls and higher rolling resistance. This energy conversion in the sidewalls increases resistance and can also lead to overheating and may have played a part in the infamous
1192:
499:
is the force needed to push (or tow) a wheeled vehicle forward (at constant speed on a level surface, or zero grade, with zero air resistance) per unit force of weight. It is assumed that all wheels are the same and bear identical weight. Thus:
2147:
A small percentage slip can result in a slip resistance which is much larger than the basic rolling resistance. For example, for pneumatic tires, a 5% slip can translate into a 200% increase in rolling resistance. This is partly because the
253:
Materials that have a large hysteresis effect, such as rubber, which bounce back slowly, exhibit more rolling resistance than materials with a small hysteresis effect that bounce back more quickly and more completely, such as steel or
3778:
Association of
American Railroads, Mechanical Division "Car and Locomotive Encyclopedia", New York, Simmons-Boardman, 1974. Section 14: "Axle journals and bearings". Almost all of the ads in this section are for the tapered type of
2194:
drops resulting in the wheel spinning even faster. This is the type of slipping that is observable by eye—the slip of say 2% for traction is only observed by instruments. Such rapid slip may result in excessive wear or damage.
854:"Rolling resistance coefficient (RRC). The value of the rolling resistance force divided by the wheel load. The Society of Automotive Engineers (SAE) has developed test practices to measure the RRC of tires. These tests (
3581:
302:
and wheel bearing friction, non-pure rolling resistance doesn't seem to have been investigated, possibly because the "pure" rolling resistance of a rubber tire is several times higher than the neglected resistances.
262:
typically incorporate silica in place of carbon black in their tread compounds to reduce low-frequency hysteresis without compromising traction. Note that railroads also have hysteresis in the roadbed structure.
3602:
A Relationship between Tyre
Pressure and Rolling Resistance Force under Different Vehicle Speed | Apiwat Suyabodha |Department of Automotive Engineering, Rangsit University, Lak-hok, Pathumthani, Thailand |
165:. Factors that contribute to rolling resistance are the (amount of) deformation of the wheels, the deformation of the roadbed surface, and movement below the surface. Additional contributing factors include
279:. This includes the increased power required due to the increased velocity of the wheels where the tangential velocity of the driving wheel(s) becomes greater than the vehicle speed due to slippage. Since
2299:
Rolling friction generates sound (vibrational) energy, as mechanical energy is converted to this form of energy due to the friction. One of the most common examples of rolling friction is the movement of
3809:"Сопротивление движению железнодорожного подвижного состава" (Resistance to motion of railway rolling stock) Труды ЦНИИ МПС (ISSN 0372-3305). Выпуск 311 (Vol. 311). - Москва: Транспорт, 1966. – 178 pp.
298:
For highway motor vehicles, there is some energy dissipated in shaking the roadway (and the earth beneath it), the shaking of the vehicle itself, and the sliding of the tires. But, other than the
61:
is the wheel radius, and both friction with the ground and friction at the axle are assumed to be negligible and so are not shown. The wheel is rolling to the left at constant speed.) Note that
1071:
2026:
142:, rolling resistance is often expressed as a coefficient times the normal force. This coefficient of rolling resistance is generally much smaller than the coefficient of sliding friction.
2373:
Virtually all world speed records have been set on relatively narrow wheels, probably because of their aerodynamic advantage at high speed, which is much less important at normal speeds.
539:
means that it would only take 0.01 pounds to tow a vehicle weighing one pound. For a 1000-pound vehicle, it would take 1000 times more tow force, i.e. 10 pounds. One could say that
987:
3862:
2731:
1339:
2642:"Tires and Passenger Vehicle Fuel Economy: Informing Consumers, Improving Performance -- Special Report 286. National Academy of Sciences, Transportation Research Board, 2006"
2914:Астахов, Figs. 3.8, 3.9, 3.11, pp. 50-55; Figs. 2.3, 2.4 pp. 35-36. (Worst case is 0.0024 for an axle load of 5.95 tonnes with obsolete plain (friction --not roller) bearings
917:
2117:
537:
727:
351:
3418:
3363:Астахов, Figs. 3.8, 3.9, 3.11, pp. 50-55. Hay, Fig. 60-2, p. 72 shows the same phenomena but has higher values for Crr and not reported here since the railroads in 2011
661:
106:
effects; that is, not all the energy needed for deformation (or movement) of the wheel, roadbed, etc., is recovered when the pressure is removed. Two forms of this are
3840:
Hoerner, Sighard F., "Fluid dynamic drag", published by the author, 1965. (Chapt. 12 is "Land-Borne
Vehicles" and includes rolling resistance (trains, autos, trucks).)
2078:
1549:
1629:
1579:
1272:
1066:
836:
806:
764:
691:
627:
597:
567:
497:
426:
2971:
Regulation (EU) 2020/740 of the
European Parliament and of the Council of 25 May 2020 on the labelling of tyres with respect to fuel efficiency and other parameters
2056:
1976:
3798:
tons-gross/tons-net, divide gross ton-mi (including locomotives) (in the "operating statistics" table by the revenue ton-miles (from the "Freight traffic" table)
3229:
Sina, Naser; Hairi Yazdi, Mohammad Reza; Esfahanian, Vahid (2020-03-01). "A novel method to improve vehicle energy efficiency: Minimization of tire power loss".
3075:
Some think that smaller tire wheels, all else being equal, tend to have higher rolling resistance than larger wheels. In some laboratory tests, however, such as
67:
is the resultant force from non-uniform pressure at the wheel-roadbed contact surface. This pressure is greater towards the front of the wheel due to hysteresis.
3518:
3498:
3478:
3458:
3438:
3100:"Three-dimensional boundary element formulation of an incompressible viscoelastic layer of finite thickness applied to the rolling resistance of a rigid sphere"
2970:
1949:
1649:
1599:
1516:
1496:
1468:
1436:
1406:
1384:
1362:
1293:
1237:
1215:
1032:
1010:
460:
394:
374:
3877:
2221:
If Crr is itself dependent on wheel load per an inverse square-root rule, then for an increase in load of 2% only a 1% increase in rolling resistance occurs.
1920:
For pneumatic tires on hard pavement, it is reported that the effect of diameter on rolling resistance is negligible (within a practical range of diameters).
4409:
2344:
2332:
Dimensions - rolling resistance in tires is related to the flex of sidewalls and the contact area of the tire For example, at the same pressure, wider
2152:
applied during this slip is many times greater than the rolling resistance force and thus much more power per unit velocity is being applied (recall
2981:
3527:
3364:
2691:
2666:
2329:
reduce rolling resistance in high performance rubber tires. Solvents may also be used to swell solid tires, decreasing the rolling resistance.
2163:
is about 40% of the maximum traction, the slip resistance is almost equal to the basic rolling resistance (hysteresis loss). But in case of a
941:
The coefficient of rolling resistance for a slow rigid wheel on a perfectly elastic surface, not adjusted for velocity, can be calculated by
3669:
2817:
3872:
221:
the hysteresis energy loss as heat. Hysteresis is the main cause of energy loss associated with rolling resistance and is attributed to the
933:
The results of these tests can be hard for the general public to obtain as manufacturers prefer to publicize "comfort" and "performance".
2263:
due to the banking, then there will be a net unbalanced sideways force on the vehicle. This will result in increased rolling resistance.
2738:
2377:
Racers heat their tires before racing, but this is primarily used to increase tire friction rather than to decrease rolling resistance.
599:
is dimensionless. Multiply it by 100 and you get the percent (%) of the weight of the vehicle required to maintain slow steady speed.
1981:
3000:
2894:
2584:
204:
3600:
4308:
3904:
1470:
seems to be based on the discredited "Coulomb's law" (Neither
Coulomb's inverse square law nor Coulomb's law of friction). See
2179:
to the wheels, some slippage of the wheel is required. For trains climbing up a grade, this slip is normally 1.5% to 2.5%.
208:
Asymmetrical pressure distribution between rolling cylinders due to viscoelastic material behavior (rolling to the right).
4298:
2601:"User guide for CONTACT, Rolling and sliding contact with friction. Technical report TR09-03 version v16.1. VORtech, 2016"
944:
4516:
4511:
4501:
3274:"Effects of resistive loads and tire inflation pressure on tire power losses and CO2 emissions in real-world conditions"
2456:
259:
119:
2958:
1306:
4419:
3939:
2218:
Crr for a rigid wheel rolling on an elastic roadbed shows Crr inversely proportional to the square root of the load.
866:. In the latter two cases, the effect of air resistance must be subtracted or the tests performed at very low speeds.
3695:
4521:
4506:
2366:
Diameter effects seem to be negligible, provided the pavement is hard and the range of diameters is limited. See
2167:
equal to 70% of the maximum traction, slip resistance becomes 10 times larger than the basic rolling resistance.
878:
314:
185:
2336:
flex less in the sidewalls as they roll and thus have lower rolling resistance (although higher air resistance).
2133:
4260:
4217:
4147:
3133:"Simple algorithms for solving steady-state frictional rolling contact problems in two and three dimensions"
3085:
2474:
2451:
2415:
2411:
2325:
As mentioned in the introduction: wheel radius, forward speed, surface adhesion, and relative micro-sliding.
1788:
Production bicycle tires at 120 psi (8.3 bar) and 50 km/h (31 mph), measured on rollers
1187:{\displaystyle C_{rr}=0.0048(18/D)^{\frac {1}{2}}(100/W)^{\frac {1}{4}}={\frac {0.0643988}{\sqrt{WD^{2}}}}}
173:, surface adhesion, sliding, and relative micro-sliding between the surfaces of contact. The losses due to
4356:
4227:
4222:
3273:
2435:
2276:
2176:
4207:
3521:
2942:
4187:
3626:
2468:
1894:
For example, in earth gravity, a car of 1000 kg on asphalt will need a force of around 100
884:
863:
177:
also depend strongly on the material properties of the wheel or tire and the surface. For example, a
103:
2663:
2623:
A handbook for the rolling resistance of pneumatic tires Clark, Samuel Kelly; Dodge, Richard N. 1979
926:
693:
is also the force per unit mass in such units. The SI system would use N/tonne (N/T, N/t), which is
4313:
3949:
3897:
2087:
503:
115:
4466:
2535:
4351:
3843:
Roberts, G. B., "Power wastage in tires", International Rubber
Conference, Washington, D.C. 1959.
3642:
3254:
3231:
Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering
2461:
2141:
696:
275:
But there is an even broader sense that would include energy wasted by wheel slippage due to the
35:
3867:
3727:
3387:
2576:
633:
4177:
4054:
3665:
3293:
3246:
2996:
2890:
2813:
2580:
2260:
2256:
2063:
1521:
4470:
4429:
4401:
4343:
4283:
4275:
4242:
4232:
4142:
4129:
4074:
4064:
4004:
3994:
3974:
3921:
3846:
U.S National Bureau of Standards, "Mechanics of Pneumatic Tires", Monograph #132, 1969–1970.
3714:
3634:
3319:
3285:
3238:
3205:
3177:
3144:
3111:
2504:
2280:
2272:
2268:
1604:
1554:
1247:
1041:
811:
781:
739:
666:
602:
572:
542:
472:
401:
247:
162:
139:
83:
2712:Астахов, Chapt. IV, p. 73+; Деев, Sect. 5.2 p. 78+; Hay, Chapt. 6 "Train Resistance" p. 67+
2034:
1954:
4212:
4172:
4162:
4157:
4097:
4039:
2670:
2288:
2153:
280:
222:
2600:
1978:
and maintain steady speed on level ground (with no air resistance) can be calculated by:
149:
will gradually slow down due to rolling resistance including that of the bearings, but a
3630:
2529:
4480:
4391:
4381:
4371:
4197:
4117:
4009:
3890:
3826:
3756:Астахов, p. 74, Although Астахов list these components, he doesn't give the sum a name.
3503:
3483:
3463:
3443:
3423:
3080:
2875:
2784:
2569:
2187:
2164:
2160:
2149:
2121:
1934:
1634:
1584:
1501:
1481:
1453:
1421:
1391:
1369:
1347:
1278:
1222:
1200:
1017:
995:
445:
379:
359:
239:
3076:
2406:
Wheel bearing torque losses can be measured as a rolling resistance at the wheel rim,
4495:
4288:
4255:
4152:
4137:
3984:
3944:
3929:
3820:"Тяга поездов" (Traction of trains) Учебное пособие. - М.: Транспорт, 1987. - 264 pp.
3646:
3258:
2341:
2309:
2301:
2244:
2191:
2183:
1895:
238:
The resulting pressure distribution is asymmetrical and is shifted to the right. The
3684:
3311:
3197:
2905:
Hay, Fig. 6-2 p.72(worst case shown of 0.0036 not used since it is likely erroneous)
2641:
2622:
2496:
569:
is in lb(tow-force)/lb(vehicle weight). Since this lb/lb is force divided by force,
283:
and the wheel velocity has increased, the power required has increased accordingly.
34:
Figure 1 Hard wheel rolling on and deforming a soft surface, resulting in the
30:
4414:
4328:
4323:
4293:
4202:
4112:
4107:
4049:
4029:
4024:
3954:
3289:
3182:
3165:
3149:
3132:
3116:
3099:
2333:
2264:
2252:
2204:
torque is not linear, but increases at a faster rate as the torque becomes higher.
1813:
1742:
463:
3810:
3769:(Railway cars). Москва, Транспорт, 1980. pp. 122 and figs. VI.1 p. 123 VI.2 p. 125
2132:"Applied torque" may either be driving torque applied by a motor (often through a
2251:) goes around a curve, rolling resistance usually increases. If the curve is not
4442:
4366:
4318:
4303:
4250:
4019:
3999:
3989:
3934:
154:
17:
3696:
http://www.rubberchemtechnol.org/resource/1/rctea4/v3/i1/p19_s1?isAuthorized=no
2386:
In a broad sense rolling resistance can be defined as the sum of components):
4447:
4265:
4192:
4102:
4092:
4059:
3345:
Roberts, Fig. 17: "Effect of torque transmission on rolling resistance", p. 71
2359:
213:
174:
107:
3297:
3250:
3242:
2321:
Several factors affect the magnitude of rolling resistance a tire generates:
808:
itself varies with those factors. It might seem from the above definition of
4437:
4386:
4376:
4333:
4082:
4044:
4034:
3969:
3964:
3576:{\displaystyle {\operatorname {d} N \over N}=2{\operatorname {d} F \over F}}
1738:
859:
855:
2851:
2531:
Elements of Mechanics: For the Use of Colleges, Academies, and High Schools
1898:
for rolling (1000 kg × 9.81 m/s × 0.01 = 98.1 N).
1878:
Stage coach (19th century) on dirt road. Soft snow on road for worst case.
838:
that the rolling resistance is directly proportional to vehicle weight but
311:
The "rolling resistance coefficient" is defined by the following equation:
3323:
3209:
2508:
1660:
850:
There are at least two popular models for calculating rolling resistance.
4087:
3979:
2465:
1735:
1450:
The above equation, where resistance is inversely proportional to radius
246:
no longer passes through the centers of the cylinders. This means that a
193:
132:
2991:
2989:
2431:
savings of the lower rolling resistance was lost to its greater weight.
4361:
4167:
3638:
3614:
2305:
733:
is the acceleration of gravity in SI units (meters per second square).
466:, the force perpendicular to the surface on which the wheel is rolling.
295:
surface, the surface changes shape and causes deformation of the tire.
146:
99:
1929:
920:
874:
255:
1760:
Railroad steel wheel on steel rail. Passenger rail car about 0.0020
135:, therefore the name "rolling friction" is to an extent a misnomer.
2889:
Roche, Schinkel, Storey, Humphris & Guelden, "Speed of Light."
3959:
3728:
The Recumbent Bicycle and Human Powered Vehicle Information Center
2248:
2137:
1836:
EU passenger car tyre label fuel efficiency class A (upper limit)
1303:
with dimension of length. It is defined by the following formula:
243:
203:
182:
150:
95:
29:
3813:(In 2012, full text was on the Internet but the U.S. was blocked)
3460:
is the normal load force on the wheel due to vehicle weight, and
4452:
4014:
3913:
2284:
189:
178:
91:
87:
3886:
1551:. Therefore, if a source gives rolling resistance coefficient (
919:) equal to the value of the rolling resistance force times the
158:
43:
from the surface having a component that opposes the motion. (
3480:
is a constant. It can be readily shown by differentiation of
2434:
An example of a very light high-speed passenger train is the
2287:
it has (at least once) been called rolling resistance due to
123:
resultant slip between the wheel and ground, which is called
3272:
Sina, Naser; Nasiri, Sayyad; Karkhaneh, Vahid (2015-11-01).
196:. Sole rolling resistance factor is not dependent on speed.
3823:
Hay, William W. "Railroad Engineering" New York, Wiley 1953
2422:
Comparing rolling resistance of highway vehicles and trains
181:
will have higher rolling resistance on a paved road than a
3166:"Simplified approaches to viscoelastic rolling resistance"
2410:. Railroads normally use roller bearings which are either
212:
The primary cause of pneumatic tire rolling resistance is
3660:
Stachowiak, Gwidon W.; Batchelor, Andrew William (2000).
3057:
Hersey, subsection: "Coulomb on wooden cylinders", p. 260
3048:
Williams, 1994, Ch. "Rolling contacts", eq. 11.1, p. 409.
2471:, the elimination of rolling and thus rolling resistance)
1581:) as a dimensionless coefficient, it can be converted to
131:
In addition, only the so-called slip resistance involves
27:
Force resisting the motion when a body rolls on a surface
3882:
118:
of the object or the surface (e.g. soil). Note that the
2402:
Loss of energy to oscillation of railway rolling stock.
766:
but does not explicitly show any variation with speed,
3873:
Simple roll-down test to measure Crr in cars and bikes
3851:
Engineering tribology'. Oxford University Press, 1994.
2969:
Annex 1, Part A. Category C1 tyres (passenger car) of
2575:(Eleventh ed.). Pearson, Prentice Hall. pp.
1798:
Dirty tram rails (standard) with straights and curves
3738:
U.S National Bureau of Standards p.? and Williams p.?
3530:
3506:
3486:
3466:
3446:
3426:
3390:
3036:
Hersey, subsection: "Static rolling friction", p.266.
2090:
2066:
2037:
1984:
1957:
1937:
1637:
1607:
1587:
1557:
1524:
1504:
1484:
1456:
1424:
1394:
1372:
1350:
1309:
1281:
1250:
1225:
1203:
1074:
1044:
1020:
998:
947:
887:
814:
784:
742:
699:
669:
636:
605:
575:
545:
506:
475:
448:
404:
382:
362:
317:
192:
on the ground will give more rolling resistance than
1364:
is the rolling resistance force (shown in figure 1),
4428:
4400:
4342:
4274:
4241:
4128:
4073:
3920:
2664:
Tyres-Online: The Benefits of Silica in Tyre Design
2407:
1475:
1244:
3575:
3512:
3492:
3472:
3452:
3432:
3412:
2568:
2111:
2072:
2058:is the linear speed of the body (at the axle), and
2050:
2020:
1970:
1943:
1659:Table of rolling resistance coefficient examples:
1643:
1623:
1593:
1573:
1543:
1510:
1490:
1462:
1430:
1400:
1378:
1356:
1333:
1287:
1266:
1231:
1209:
1186:
1060:
1026:
1004:
981:
911:
830:
800:
758:
721:
685:
655:
621:
591:
561:
531:
491:
454:
420:
388:
368:
345:
3685:http://144.206.159.178/ft/200/607426/12614863.pdf
3341:
3339:
3077:Greenspeed test results (accessdate = 2007-10-27)
1068:for cast iron mine car wheels on steel rails is:
771:
3366:. were claiming about the same value as Астахов
3164:Zéhil, Gérard-Philippe; Gavin, Henri P. (2013).
3131:Zéhil, Gérard-Philippe; Gavin, Henri P. (2013).
3098:Zéhil, Gérard-Philippe; Gavin, Henri P. (2013).
2764:kgf/tonne is used by Астахов throughout his book
1474:. Equating this equation with the force per the
250:occurs that tends to retard the rolling motion.
2186:) is normally roughly directly proportional to
2159:It is shown that for a passenger car, when the
2021:{\displaystyle T={\frac {V_{s}}{\Omega }}R_{r}}
3664:(2. ed.). Oxford: Butterworth-Heinemann.
3170:International Journal of Solids and Structures
3137:International Journal of Solids and Structures
3104:International Journal of Solids and Structures
1826:Typical BMX bicycle tires used for solar cars
299:
276:
161:of the same mass with rubber tires running on
3898:
3027:Hersey, subsection: "End of dark ages", p.261
2885:
2883:
2571:Engineering Mechanics: Statics & Dynamics
2491:
2489:
2124:, coefficient of friction, normal load, etc.
929:is used to test rolling resistance in Europe.
839:
767:
170:
8:
4410:European Tyre and Rim Technical Organisation
3066:U.S. National Bureau of Standards, Fig. 1.13
2546:rolling friction less than sliding friction.
2534:. A.S. Barnes & Burr: New York. p.
3709:
3707:
3705:
3703:
3354:Деев, p.30 including eq. (2.7) and Fig. 2.3
3044:
3042:
3013:
3011:
3009:
2382:Railroads: Components of rolling resistance
2367:
1471:
775:
736:The above shows resistance proportional to
166:
3905:
3891:
3883:
2690:An example of such usage for railroads is
2562:
2560:
2558:
2556:
2554:
2399:Loss of energy to the roadbed (and earth).
376:is the rolling resistance force (shown as
55:is some towing force applied to the axle,
3555:
3531:
3529:
3505:
3485:
3465:
3445:
3425:
3404:
3389:
3181:
3148:
3115:
2101:
2095:
2089:
2065:
2042:
2036:
2012:
1997:
1991:
1983:
1962:
1956:
1936:
1636:
1612:
1606:
1601:, having units of length, by multiplying
1586:
1562:
1556:
1529:
1523:
1503:
1483:
1455:
1423:
1393:
1371:
1349:
1316:
1308:
1280:
1255:
1249:
1224:
1202:
1176:
1169:
1155:
1141:
1129:
1112:
1100:
1079:
1073:
1049:
1043:
1019:
997:
969:
964:
952:
946:
886:
819:
813:
789:
783:
747:
741:
710:
698:
674:
668:
644:
635:
610:
604:
580:
574:
550:
544:
514:
505:
480:
474:
447:
409:
403:
381:
361:
331:
316:
2876:ETH - PAC-Car II vs PAC-Car I - Technics
2636:
2634:
2632:
2630:
1774:Mine car cast iron wheels on steel rail
1663:
1239:is the load on the wheel in pounds-force
2485:
1655:Rolling resistance coefficient examples
923:of the wheel divided by the wheel load.
300:additional power required due to torque
153:car with steel wheels running on steel
3747:Roberts, "Effect of temperature", p.59
2959:Crr for large truck tires per Michelin
2773:Деев uses N/T notation. See pp. 78-84.
1720:Hardened steel ball bearings on steel
869:The coefficient of rolling resistance
281:power is equal to force times velocity
2852:"Coefficients of Friction in Bearing"
778:, tire inflation/wear, etc., because
291:this broad-sense rolling resistance.
102:on a surface. It is mainly caused by
7:
3715:"Schwalbe Tires: Rolling Resistance"
3440:is the rolling resistance force and
2732:"Rolling Resistance and Fuel Saving"
982:{\displaystyle C_{rr}={\sqrt {z/d}}}
4453:Uniform Tire Quality Grading (UTQG)
3816:Деев В.В., Ильин Г.А., Афонин Г.С.
1705:Railroad steel wheel on steel rail
49:is some vertical load on the axle,
3863:Rolling Resistance and Fuel Saving
3833:, April 1969 pp. 260–275 and
3558:
3534:
2234:Dependence on curvature of roadway
2106:
2067:
2003:
1034:is the diameter of the rigid wheel
729:and is force per unit mass, where
111:
25:
3868:temperature vs rolling resistance
3835:Journal of Lubrication Technology
2808:Guiggiani, Massimo (5 May 2018).
2396:Sliding of the wheel on the rail.
2279:). For railroads, this is called
2136:) or a braking torque applied by
1334:{\displaystyle F={\frac {Nb}{r}}}
4476:
4475:
4465:
2427:cases they may be much lighter.
2317:Factors that contribute in tires
1702:
4309:Tire-pressure monitoring system
2810:The Science of Vehicle Dynamics
1951:to overcome rolling resistance
1864:Ordinary car tires on concrete
1414:coefficient of rolling friction
1301:coefficient of rolling friction
1217:is the wheel diameter in inches
912:{\displaystyle \cos(\theta )=1}
877:, is approximately (due to the
434:coefficient of rolling friction
3765:Шадур. Л. А. (editor). Вагоны
3619:Water, Air, and Soil Pollution
3290:10.1016/j.apenergy.2015.04.010
3183:10.1016/j.ijsolstr.2012.09.025
3150:10.1016/j.ijsolstr.2012.11.021
3117:10.1016/j.ijsolstr.2012.11.020
1476:rolling resistance coefficient
1438:is the normal force (equal to
1410:rolling resistance coefficient
1297:rolling resistance coefficient
1138:
1123:
1109:
1094:
900:
894:
430:rolling resistance coefficient
307:Rolling resistance coefficient
277:torque applied from the engine
229:— National Academy of Sciences
1:
4299:Central Tire Inflation System
3878:Rolling Resistance Thresholds
2812:. Springer Cham. p. 22.
2255:so as to exactly counter the
2112:{\displaystyle V_{s}/\Omega }
1416:with dimension of length, and
873:, which has the dimension of
532:{\displaystyle \ C_{rr}=0.01}
82:, is the force resisting the
2457:Low-rolling resistance tires
2390:Wheel bearing torque losses.
2308:, a process which generates
1924:Dependence on applied torque
1665:
260:Low rolling resistance tires
223:viscoelastic characteristics
4420:Tire Science and Technology
3940:Low rolling resistance tire
3811:perm. record at UC Berkeley
3615:"Analysis of highway noise"
2832:Hersey, equation (2), p. 83
2259:with an equal and opposing
1888:Ordinary car tires on sand
1243:As an alternative to using
722:{\displaystyle 1000gC_{rr}}
346:{\displaystyle \ F=C_{rr}N}
4538:
3613:Hogan, C. Michael (1973).
3413:{\displaystyle F=kN^{0.5}}
2721:Астахов, Fig. 4.14, p. 107
2528:Peck, William Guy (1859).
2269:"superelevation" or "cant"
1907:Stagecoaches and railroads
1038:The empirical formula for
656:{\displaystyle 2000C_{rr}}
4461:
2271:(not to be confused with
1703:"Pure rolling resistance"
879:small-angle approximation
157:will roll farther than a
3831:Transactions of the ASME
3375:Hersey, Table 6., p. 267
3243:10.1177/0954407019861241
2856:Coefficients of Friction
2393:Pure rolling resistance.
2208:Dependence on wheel load
1446:, as shown in figure 1).
4261:Slip (vehicle dynamics)
4218:Lateral Force Variation
4168:Pacejka's Magic Formula
4148:Cold inflation pressure
3788:Астахов, Fig 4.2, p. 76
2923:Астахов, Fig. 2.1, p.22
2703:Деев, p. 79. Hay, p. 68
2567:Hibbeler, R.C. (2007).
2475:Rolling element bearing
2452:Coefficient of friction
2073:{\displaystyle \Omega }
1544:{\displaystyle C_{rr}r}
1295:, which is a different
188:on a steel rail. Also,
86:when a body (such as a
4357:List of tire companies
4228:Traction (engineering)
4223:Radial Force Variation
3577:
3514:
3494:
3474:
3454:
3434:
3414:
2982:Green Seal 2003 Report
2932:Hersey, Table 6, p.267
2789:www.biketechreview.com
2436:N700 Series Shinkansen
2368:dependence on diameter
2175:In order to apply any
2113:
2084:It is noteworthy that
2074:
2052:
2022:
1972:
1945:
1902:Dependence on diameter
1850:Car tire measurements
1645:
1625:
1624:{\displaystyle C_{rr}}
1595:
1575:
1574:{\displaystyle C_{rr}}
1545:
1512:
1492:
1472:dependence on diameter
1464:
1432:
1402:
1380:
1358:
1335:
1289:
1268:
1267:{\displaystyle C_{rr}}
1233:
1211:
1188:
1062:
1061:{\displaystyle C_{rr}}
1028:
1006:
983:
913:
832:
831:{\displaystyle C_{rr}}
802:
801:{\displaystyle C_{rr}}
760:
759:{\displaystyle C_{rr}}
723:
687:
686:{\displaystyle C_{rr}}
657:
623:
622:{\displaystyle C_{rr}}
593:
592:{\displaystyle C_{rr}}
563:
562:{\displaystyle C_{rr}}
533:
493:
492:{\displaystyle C_{rr}}
456:
422:
421:{\displaystyle C_{rr}}
390:
370:
347:
232:
209:
68:
4208:Tire load sensitivity
3829:, "Rolling Friction"
3662:Engineering tribology
3578:
3515:
3495:
3475:
3455:
3435:
3415:
3384:Per this assumption,
3324:10.4271/06-11-02-0014
3210:10.4271/06-11-02-0014
2509:10.4271/06-11-02-0014
2213:Railroad steel wheels
2171:Railroad steel wheels
2114:
2080:its rotational speed.
2075:
2053:
2051:{\displaystyle V_{s}}
2023:
1973:
1971:{\displaystyle R_{r}}
1946:
1646:
1626:
1596:
1576:
1546:
1513:
1493:
1465:
1433:
1403:
1381:
1359:
1336:
1290:
1269:
1234:
1212:
1189:
1063:
1029:
1007:
984:
914:
833:
803:
774:, surface roughness,
761:
724:
688:
658:
624:
594:
564:
534:
494:
457:
428:is the dimensionless
423:
391:
371:
348:
218:
207:
145:Any coasting wheeled
116:(plastic) deformation
33:
4188:Self aligning torque
3528:
3504:
3484:
3464:
3444:
3424:
3388:
3084:controlled for. See
2182:Slip (also known as
2142:regenerative braking
2088:
2064:
2035:
1982:
1955:
1935:
1635:
1605:
1585:
1555:
1522:
1502:
1482:
1454:
1422:
1392:
1386:is the wheel radius,
1370:
1348:
1307:
1279:
1248:
1223:
1201:
1072:
1042:
1018:
1012:is the sinkage depth
996:
945:
885:
812:
782:
740:
697:
667:
634:
603:
573:
543:
504:
473:
446:
402:
380:
360:
315:
4517:Transport economics
4512:Energy in transport
4502:Classical mechanics
4314:Tire-pressure gauge
3950:Michelin PAX System
3631:1973WASP....2..387H
3591:Roberts, pp. 60-61.
242:of the (aggregate)
74:, sometimes called
4352:Tire manufacturing
4183:Rolling resistance
3639:10.1007/BF00159677
3573:
3510:
3490:
3470:
3450:
3430:
3410:
3316:saemobilus.sae.org
3202:saemobilus.sae.org
2669:2013-02-04 at the
2501:saemobilus.sae.org
2345:rollover accidents
2109:
2070:
2048:
2018:
1968:
1941:
1641:
1621:
1591:
1571:
1541:
1508:
1488:
1478:, and solving for
1460:
1428:
1398:
1376:
1354:
1331:
1285:
1264:
1229:
1207:
1184:
1058:
1024:
1002:
979:
909:
828:
798:
756:
719:
683:
653:
619:
589:
559:
529:
489:
452:
418:
386:
366:
343:
210:
72:Rolling resistance
69:
4489:
4488:
4178:Relaxation length
4055:Formula One tyres
3671:978-0-7506-7304-4
3571:
3547:
3513:{\displaystyle N}
3493:{\displaystyle F}
3473:{\displaystyle k}
3453:{\displaystyle N}
3433:{\displaystyle F}
2819:978-3-319-73220-6
2267:is also known as
2261:centripetal force
2257:centrifugal force
2006:
1944:{\displaystyle T}
1892:
1891:
1644:{\displaystyle r}
1594:{\displaystyle b}
1511:{\displaystyle b}
1491:{\displaystyle b}
1463:{\displaystyle r}
1431:{\displaystyle N}
1401:{\displaystyle b}
1379:{\displaystyle r}
1357:{\displaystyle F}
1329:
1288:{\displaystyle b}
1232:{\displaystyle W}
1210:{\displaystyle D}
1182:
1181:
1149:
1120:
1027:{\displaystyle d}
1005:{\displaystyle z}
977:
937:Physical formulae
509:
455:{\displaystyle N}
389:{\displaystyle R}
369:{\displaystyle F}
320:
114:), and permanent
16:(Redirected from
4529:
4522:Vehicle dynamics
4507:Energy economics
4479:
4478:
4471:Outline of tires
4469:
4284:Tire maintenance
4233:Treadwear rating
4143:Circle of forces
4065:Continental tire
4005:Orange oil tires
3995:Mud-terrain tire
3975:All-terrain tire
3907:
3900:
3893:
3884:
3849:Williams, J. A.
3819:
3808:
3799:
3795:
3789:
3786:
3780:
3776:
3770:
3768:
3763:
3757:
3754:
3748:
3745:
3739:
3736:
3730:
3725:
3719:
3718:
3711:
3698:
3693:
3687:
3682:
3676:
3675:
3657:
3651:
3650:
3610:
3604:
3598:
3592:
3589:
3583:
3582:
3580:
3579:
3574:
3572:
3567:
3556:
3548:
3543:
3532:
3519:
3517:
3516:
3511:
3500:with respect to
3499:
3497:
3496:
3491:
3479:
3477:
3476:
3471:
3459:
3457:
3456:
3451:
3439:
3437:
3436:
3431:
3419:
3417:
3416:
3411:
3409:
3408:
3382:
3376:
3373:
3367:
3361:
3355:
3352:
3346:
3343:
3334:
3333:
3331:
3330:
3308:
3302:
3301:
3269:
3263:
3262:
3237:(4): 1153–1166.
3226:
3220:
3219:
3217:
3216:
3194:
3188:
3187:
3185:
3161:
3155:
3154:
3152:
3128:
3122:
3121:
3119:
3095:
3089:
3073:
3067:
3064:
3058:
3055:
3049:
3046:
3037:
3034:
3028:
3025:
3019:
3015:
3004:
2993:
2984:
2979:
2973:
2967:
2961:
2956:
2950:
2949:
2947:
2939:
2933:
2930:
2924:
2921:
2915:
2912:
2906:
2903:
2897:
2887:
2878:
2873:
2867:
2866:
2864:
2862:
2848:
2842:
2839:
2833:
2830:
2824:
2823:
2805:
2799:
2798:
2796:
2795:
2783:Willett, Kraig.
2780:
2774:
2771:
2765:
2762:
2756:
2752:
2746:
2745:
2743:
2737:. Archived from
2736:
2728:
2722:
2719:
2713:
2710:
2704:
2701:
2695:
2688:
2682:
2679:
2673:
2661:
2655:
2654:
2652:
2651:
2646:
2638:
2625:
2620:
2614:
2613:
2611:
2610:
2605:
2597:
2591:
2590:
2574:
2564:
2549:
2548:
2543:
2542:
2525:
2519:
2518:
2516:
2515:
2493:
2281:curve resistance
2243:When a vehicle (
2118:
2116:
2115:
2110:
2105:
2100:
2099:
2079:
2077:
2076:
2071:
2057:
2055:
2054:
2049:
2047:
2046:
2027:
2025:
2024:
2019:
2017:
2016:
2007:
2002:
2001:
1992:
1977:
1975:
1974:
1969:
1967:
1966:
1950:
1948:
1947:
1942:
1664:
1650:
1648:
1647:
1642:
1631:by wheel radius
1630:
1628:
1627:
1622:
1620:
1619:
1600:
1598:
1597:
1592:
1580:
1578:
1577:
1572:
1570:
1569:
1550:
1548:
1547:
1542:
1537:
1536:
1517:
1515:
1514:
1509:
1497:
1495:
1494:
1489:
1469:
1467:
1466:
1461:
1437:
1435:
1434:
1429:
1407:
1405:
1404:
1399:
1385:
1383:
1382:
1377:
1363:
1361:
1360:
1355:
1340:
1338:
1337:
1332:
1330:
1325:
1317:
1294:
1292:
1291:
1286:
1273:
1271:
1270:
1265:
1263:
1262:
1238:
1236:
1235:
1230:
1216:
1214:
1213:
1208:
1193:
1191:
1190:
1185:
1183:
1180:
1175:
1174:
1173:
1160:
1156:
1151:
1150:
1142:
1133:
1122:
1121:
1113:
1104:
1087:
1086:
1067:
1065:
1064:
1059:
1057:
1056:
1033:
1031:
1030:
1025:
1011:
1009:
1008:
1003:
988:
986:
985:
980:
978:
973:
965:
960:
959:
918:
916:
915:
910:
864:coast-down tests
837:
835:
834:
829:
827:
826:
807:
805:
804:
799:
797:
796:
765:
763:
762:
757:
755:
754:
728:
726:
725:
720:
718:
717:
692:
690:
689:
684:
682:
681:
662:
660:
659:
654:
652:
651:
628:
626:
625:
620:
618:
617:
598:
596:
595:
590:
588:
587:
568:
566:
565:
560:
558:
557:
538:
536:
535:
530:
522:
521:
507:
498:
496:
495:
490:
488:
487:
461:
459:
458:
453:
427:
425:
424:
419:
417:
416:
395:
393:
392:
387:
375:
373:
372:
367:
352:
350:
349:
344:
339:
338:
318:
140:sliding friction
129:slip resistance.
76:rolling friction
21:
18:Rolling friction
4537:
4536:
4532:
4531:
4530:
4528:
4527:
4526:
4492:
4491:
4490:
4485:
4457:
4424:
4396:
4338:
4270:
4237:
4213:Tire uniformity
4173:Pneumatic trail
4163:Ground pressure
4158:Cornering force
4124:
4098:Siping (rubber)
4069:
4040:Motorcycle tyre
3916:
3911:
3859:
3827:Hersey, Mayo D.
3817:
3806:
3802:
3796:
3792:
3787:
3783:
3777:
3773:
3766:
3764:
3760:
3755:
3751:
3746:
3742:
3737:
3733:
3726:
3722:
3713:
3712:
3701:
3694:
3690:
3683:
3679:
3672:
3659:
3658:
3654:
3612:
3611:
3607:
3599:
3595:
3590:
3586:
3557:
3533:
3526:
3525:
3502:
3501:
3482:
3481:
3462:
3461:
3442:
3441:
3422:
3421:
3400:
3386:
3385:
3383:
3379:
3374:
3370:
3362:
3358:
3353:
3349:
3344:
3337:
3328:
3326:
3310:
3309:
3305:
3271:
3270:
3266:
3228:
3227:
3223:
3214:
3212:
3196:
3195:
3191:
3163:
3162:
3158:
3130:
3129:
3125:
3097:
3096:
3092:
3074:
3070:
3065:
3061:
3056:
3052:
3047:
3040:
3035:
3031:
3026:
3022:
3016:
3007:
2994:
2987:
2980:
2976:
2968:
2964:
2957:
2953:
2945:
2941:
2940:
2936:
2931:
2927:
2922:
2918:
2913:
2909:
2904:
2900:
2888:
2881:
2874:
2870:
2860:
2858:
2850:
2849:
2845:
2841:Астахов, p. 81.
2840:
2836:
2831:
2827:
2820:
2807:
2806:
2802:
2793:
2791:
2782:
2781:
2777:
2772:
2768:
2763:
2759:
2753:
2749:
2741:
2734:
2730:
2729:
2725:
2720:
2716:
2711:
2707:
2702:
2698:
2689:
2685:
2680:
2676:
2671:Wayback Machine
2662:
2658:
2649:
2647:
2644:
2640:
2639:
2628:
2621:
2617:
2608:
2606:
2603:
2599:
2598:
2594:
2587:
2566:
2565:
2552:
2540:
2538:
2527:
2526:
2522:
2513:
2511:
2495:
2494:
2487:
2483:
2448:
2424:
2384:
2319:
2297:
2241:
2236:
2227:
2225:Pneumatic tires
2215:
2210:
2201:
2199:Pneumatic tires
2188:tractive effort
2173:
2130:
2091:
2086:
2085:
2062:
2061:
2038:
2033:
2032:
2008:
1993:
1980:
1979:
1958:
1953:
1952:
1933:
1932:
1926:
1918:
1916:Pneumatic tires
1909:
1904:
1676:
1657:
1633:
1632:
1608:
1603:
1602:
1583:
1582:
1558:
1553:
1552:
1525:
1520:
1519:
1500:
1499:
1480:
1479:
1452:
1451:
1420:
1419:
1390:
1389:
1368:
1367:
1346:
1345:
1318:
1305:
1304:
1277:
1276:
1251:
1246:
1245:
1221:
1220:
1199:
1198:
1165:
1161:
1137:
1108:
1075:
1070:
1069:
1045:
1040:
1039:
1016:
1015:
994:
993:
948:
943:
942:
939:
883:
882:
848:
815:
810:
809:
785:
780:
779:
743:
738:
737:
706:
695:
694:
670:
665:
664:
640:
632:
631:
606:
601:
600:
576:
571:
570:
546:
541:
540:
510:
502:
501:
476:
471:
470:
444:
443:
405:
400:
399:
378:
377:
358:
357:
327:
313:
312:
309:
269:
225:of the rubber.
202:
138:Analogous with
28:
23:
22:
15:
12:
11:
5:
4535:
4533:
4525:
4524:
4519:
4514:
4509:
4504:
4494:
4493:
4487:
4486:
4484:
4483:
4473:
4462:
4459:
4458:
4456:
4455:
4450:
4445:
4440:
4434:
4432:
4430:Identification
4426:
4425:
4423:
4422:
4417:
4412:
4406:
4404:
4398:
4397:
4395:
4394:
4392:Ozone cracking
4389:
4384:
4379:
4374:
4372:Tire recycling
4369:
4364:
4359:
4354:
4348:
4346:
4340:
4339:
4337:
4336:
4331:
4326:
4321:
4316:
4311:
4306:
4301:
4296:
4291:
4286:
4280:
4278:
4272:
4271:
4269:
4268:
4263:
4258:
4253:
4247:
4245:
4239:
4238:
4236:
4235:
4230:
4225:
4220:
4215:
4210:
4205:
4200:
4198:Steering ratio
4195:
4190:
4185:
4180:
4175:
4170:
4165:
4160:
4155:
4150:
4145:
4140:
4134:
4132:
4126:
4125:
4123:
4122:
4121:
4120:
4118:Schrader valve
4115:
4110:
4100:
4095:
4090:
4085:
4079:
4077:
4071:
4070:
4068:
4067:
4062:
4057:
4052:
4047:
4042:
4037:
4032:
4027:
4022:
4017:
4012:
4010:Whitewall tire
4007:
4002:
3997:
3992:
3987:
3982:
3977:
3972:
3967:
3962:
3957:
3952:
3947:
3942:
3937:
3932:
3926:
3924:
3918:
3917:
3912:
3910:
3909:
3902:
3895:
3887:
3881:
3880:
3875:
3870:
3865:
3858:
3857:External links
3855:
3854:
3853:
3847:
3844:
3841:
3838:
3824:
3821:
3814:
3801:
3800:
3790:
3781:
3771:
3758:
3749:
3740:
3731:
3720:
3699:
3688:
3677:
3670:
3652:
3625:(3): 387–392.
3605:
3593:
3584:
3570:
3566:
3563:
3560:
3554:
3551:
3546:
3542:
3539:
3536:
3509:
3489:
3469:
3449:
3429:
3407:
3403:
3399:
3396:
3393:
3377:
3368:
3356:
3347:
3335:
3303:
3278:Applied Energy
3264:
3221:
3189:
3176:(6): 853–862.
3156:
3143:(6): 843–852.
3123:
3110:(6): 833–842.
3090:
3081:ultimate speed
3068:
3059:
3050:
3038:
3029:
3020:
3005:
2985:
2974:
2962:
2951:
2934:
2925:
2916:
2907:
2898:
2879:
2868:
2843:
2834:
2825:
2818:
2800:
2775:
2766:
2757:
2747:
2744:on 2016-04-08.
2723:
2714:
2705:
2696:
2683:
2674:
2656:
2626:
2615:
2592:
2585:
2550:
2520:
2484:
2482:
2479:
2478:
2477:
2472:
2459:
2454:
2447:
2444:
2423:
2420:
2404:
2403:
2400:
2397:
2394:
2391:
2383:
2380:
2379:
2378:
2374:
2371:
2364:
2356:
2352:
2348:
2337:
2330:
2326:
2318:
2315:
2296:
2293:
2240:
2237:
2235:
2232:
2226:
2223:
2214:
2211:
2209:
2206:
2200:
2197:
2172:
2169:
2165:tractive force
2161:tractive force
2150:tractive force
2129:
2126:
2122:tractive force
2108:
2104:
2098:
2094:
2082:
2081:
2069:
2059:
2045:
2041:
2015:
2011:
2005:
2000:
1996:
1990:
1987:
1965:
1961:
1940:
1925:
1922:
1917:
1914:
1908:
1905:
1903:
1900:
1890:
1889:
1886:
1884:
1880:
1879:
1876:
1874:
1866:
1865:
1862:
1860:
1852:
1851:
1848:
1846:
1838:
1837:
1834:
1832:
1828:
1827:
1824:
1822:
1818:
1817:
1810:
1808:
1800:
1799:
1796:
1794:
1790:
1789:
1786:
1784:
1776:
1775:
1772:
1770:
1762:
1761:
1758:
1755:
1747:
1746:
1732:
1730:
1722:
1721:
1718:
1715:
1707:
1706:
1700:
1698:
1690:
1689:
1684:
1677:
1672:
1656:
1653:
1640:
1618:
1615:
1611:
1590:
1568:
1565:
1561:
1540:
1535:
1532:
1528:
1507:
1487:
1459:
1448:
1447:
1427:
1417:
1397:
1387:
1375:
1365:
1353:
1328:
1324:
1321:
1315:
1312:
1284:
1261:
1258:
1254:
1241:
1240:
1228:
1218:
1206:
1179:
1172:
1168:
1164:
1159:
1154:
1148:
1145:
1140:
1136:
1132:
1128:
1125:
1119:
1116:
1111:
1107:
1103:
1099:
1096:
1093:
1090:
1085:
1082:
1078:
1055:
1052:
1048:
1036:
1035:
1023:
1013:
1001:
976:
972:
968:
963:
958:
955:
951:
938:
935:
931:
930:
927:ISO 18164:2005
924:
908:
905:
902:
899:
896:
893:
890:
867:
847:
844:
825:
822:
818:
795:
792:
788:
753:
750:
746:
716:
713:
709:
705:
702:
680:
677:
673:
650:
647:
643:
639:
616:
613:
609:
586:
583:
579:
556:
553:
549:
528:
525:
520:
517:
513:
486:
483:
479:
468:
467:
451:
441:
415:
412:
408:
397:
385:
365:
342:
337:
334:
330:
326:
323:
308:
305:
268:
265:
244:vertical force
240:line of action
231:
230:
201:
198:
186:railroad wheel
167:wheel diameter
163:tarmac/asphalt
36:reaction force
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4534:
4523:
4520:
4518:
4515:
4513:
4510:
4508:
4505:
4503:
4500:
4499:
4497:
4482:
4474:
4472:
4468:
4464:
4463:
4460:
4454:
4451:
4449:
4446:
4444:
4441:
4439:
4436:
4435:
4433:
4431:
4427:
4421:
4418:
4416:
4413:
4411:
4408:
4407:
4405:
4403:
4402:Organizations
4399:
4393:
4390:
4388:
4385:
4383:
4380:
4378:
4375:
4373:
4370:
4368:
4365:
4363:
4360:
4358:
4355:
4353:
4350:
4349:
4347:
4345:
4341:
4335:
4332:
4330:
4327:
4325:
4322:
4320:
4317:
4315:
4312:
4310:
4307:
4305:
4302:
4300:
4297:
4295:
4292:
4290:
4289:Tire rotation
4287:
4285:
4282:
4281:
4279:
4277:
4273:
4267:
4264:
4262:
4259:
4257:
4256:Groove wander
4254:
4252:
4249:
4248:
4246:
4244:
4240:
4234:
4231:
4229:
4226:
4224:
4221:
4219:
4216:
4214:
4211:
4209:
4206:
4204:
4201:
4199:
4196:
4194:
4191:
4189:
4186:
4184:
4181:
4179:
4176:
4174:
4171:
4169:
4166:
4164:
4161:
4159:
4156:
4154:
4153:Contact patch
4151:
4149:
4146:
4144:
4141:
4139:
4138:Camber thrust
4136:
4135:
4133:
4131:
4127:
4119:
4116:
4114:
4111:
4109:
4106:
4105:
4104:
4101:
4099:
4096:
4094:
4091:
4089:
4086:
4084:
4081:
4080:
4078:
4076:
4072:
4066:
4063:
4061:
4058:
4056:
4053:
4051:
4048:
4046:
4043:
4041:
4038:
4036:
4033:
4031:
4028:
4026:
4023:
4021:
4018:
4016:
4015:Aircraft tire
4013:
4011:
4008:
4006:
4003:
4001:
3998:
3996:
3993:
3991:
3988:
3986:
3983:
3981:
3978:
3976:
3973:
3971:
3968:
3966:
3963:
3961:
3958:
3956:
3953:
3951:
3948:
3946:
3945:Run-flat tire
3943:
3941:
3938:
3936:
3933:
3931:
3930:Tubeless tire
3928:
3927:
3925:
3923:
3919:
3915:
3908:
3903:
3901:
3896:
3894:
3889:
3888:
3885:
3879:
3876:
3874:
3871:
3869:
3866:
3864:
3861:
3860:
3856:
3852:
3848:
3845:
3842:
3839:
3836:
3832:
3828:
3825:
3822:
3815:
3812:
3805:Астахов П.Н.
3804:
3803:
3794:
3791:
3785:
3782:
3775:
3772:
3762:
3759:
3753:
3750:
3744:
3741:
3735:
3732:
3729:
3724:
3721:
3716:
3710:
3708:
3706:
3704:
3700:
3697:
3692:
3689:
3686:
3681:
3678:
3673:
3667:
3663:
3656:
3653:
3648:
3644:
3640:
3636:
3632:
3628:
3624:
3620:
3616:
3609:
3606:
3601:
3597:
3594:
3588:
3585:
3568:
3564:
3561:
3552:
3549:
3544:
3540:
3537:
3523:
3507:
3487:
3467:
3447:
3427:
3405:
3401:
3397:
3394:
3391:
3381:
3378:
3372:
3369:
3365:
3360:
3357:
3351:
3348:
3342:
3340:
3336:
3325:
3321:
3317:
3313:
3312:"SAE MOBILUS"
3307:
3304:
3299:
3295:
3291:
3287:
3283:
3279:
3275:
3268:
3265:
3260:
3256:
3252:
3248:
3244:
3240:
3236:
3232:
3225:
3222:
3211:
3207:
3203:
3199:
3198:"SAE MOBILUS"
3193:
3190:
3184:
3179:
3175:
3171:
3167:
3160:
3157:
3151:
3146:
3142:
3138:
3134:
3127:
3124:
3118:
3113:
3109:
3105:
3101:
3094:
3091:
3087:
3082:
3078:
3072:
3069:
3063:
3060:
3054:
3051:
3045:
3043:
3039:
3033:
3030:
3024:
3021:
3014:
3012:
3010:
3006:
3002:
3001:1-56091-199-9
2998:
2992:
2990:
2986:
2983:
2978:
2975:
2972:
2966:
2963:
2960:
2955:
2952:
2944:
2943:"Roller Data"
2938:
2935:
2929:
2926:
2920:
2917:
2911:
2908:
2902:
2899:
2896:
2895:0-7334-1527-X
2892:
2886:
2884:
2880:
2877:
2872:
2869:
2857:
2853:
2847:
2844:
2838:
2835:
2829:
2826:
2821:
2815:
2811:
2804:
2801:
2790:
2786:
2785:"Roller Data"
2779:
2776:
2770:
2767:
2761:
2758:
2751:
2748:
2740:
2733:
2727:
2724:
2718:
2715:
2709:
2706:
2700:
2697:
2693:
2687:
2684:
2681:Астахов, p.85
2678:
2675:
2672:
2668:
2665:
2660:
2657:
2643:
2637:
2635:
2633:
2631:
2627:
2624:
2619:
2616:
2602:
2596:
2593:
2588:
2586:9780132038096
2582:
2578:
2573:
2572:
2563:
2561:
2559:
2557:
2555:
2551:
2547:
2537:
2533:
2532:
2524:
2521:
2510:
2506:
2502:
2498:
2497:"SAE MOBILUS"
2492:
2490:
2486:
2480:
2476:
2473:
2470:
2467:
2463:
2460:
2458:
2455:
2453:
2450:
2449:
2445:
2443:
2439:
2437:
2432:
2428:
2421:
2419:
2417:
2413:
2409:
2401:
2398:
2395:
2392:
2389:
2388:
2387:
2381:
2375:
2372:
2369:
2365:
2361:
2357:
2353:
2349:
2346:
2343:
2342:Ford Explorer
2338:
2335:
2334:bicycle tires
2331:
2327:
2324:
2323:
2322:
2316:
2314:
2311:
2307:
2303:
2302:motor vehicle
2294:
2292:
2290:
2286:
2282:
2278:
2274:
2270:
2266:
2262:
2258:
2254:
2250:
2246:
2245:motor vehicle
2238:
2233:
2231:
2224:
2222:
2219:
2212:
2207:
2205:
2198:
2196:
2193:
2189:
2185:
2180:
2178:
2170:
2168:
2166:
2162:
2157:
2155:
2151:
2145:
2143:
2139:
2135:
2127:
2125:
2123:
2102:
2096:
2092:
2060:
2043:
2039:
2031:
2030:
2029:
2013:
2009:
1998:
1994:
1988:
1985:
1963:
1959:
1938:
1931:
1923:
1921:
1915:
1913:
1906:
1901:
1899:
1897:
1887:
1885:
1882:
1881:
1877:
1875:
1872:
1868:
1867:
1863:
1861:
1858:
1854:
1853:
1849:
1847:
1844:
1840:
1839:
1835:
1833:
1830:
1829:
1825:
1823:
1820:
1819:
1815:
1811:
1809:
1806:
1802:
1801:
1797:
1795:
1792:
1791:
1787:
1785:
1782:
1778:
1777:
1773:
1771:
1768:
1764:
1763:
1759:
1756:
1753:
1749:
1748:
1744:
1740:
1737:
1733:
1731:
1728:
1724:
1723:
1719:
1716:
1713:
1709:
1708:
1704:
1701:
1699:
1696:
1692:
1691:
1688:
1685:
1683:
1682:
1678:
1675:
1671:
1670:
1666:
1662:
1661:
1654:
1652:
1638:
1616:
1613:
1609:
1588:
1566:
1563:
1559:
1538:
1533:
1530:
1526:
1505:
1485:
1477:
1473:
1457:
1445:
1441:
1425:
1418:
1415:
1411:
1395:
1388:
1373:
1366:
1351:
1344:
1343:
1342:
1326:
1322:
1319:
1313:
1310:
1302:
1298:
1282:
1274:
1259:
1256:
1252:
1226:
1219:
1204:
1197:
1196:
1195:
1177:
1170:
1166:
1162:
1157:
1152:
1146:
1143:
1134:
1130:
1126:
1117:
1114:
1105:
1101:
1097:
1091:
1088:
1083:
1080:
1076:
1053:
1050:
1046:
1021:
1014:
999:
992:
991:
990:
974:
970:
966:
961:
956:
953:
949:
936:
934:
928:
925:
922:
906:
903:
897:
891:
888:
880:
876:
872:
868:
865:
861:
857:
853:
852:
851:
845:
843:
841:
823:
820:
816:
793:
790:
786:
777:
773:
769:
751:
748:
744:
734:
732:
714:
711:
707:
703:
700:
678:
675:
671:
648:
645:
641:
637:
614:
611:
607:
584:
581:
577:
554:
551:
547:
526:
523:
518:
515:
511:
484:
481:
477:
465:
449:
442:
439:
435:
431:
413:
410:
406:
398:
396:in figure 1),
383:
363:
356:
355:
354:
340:
335:
332:
328:
324:
321:
306:
304:
301:
296:
292:
288:
284:
282:
278:
273:
266:
264:
261:
257:
251:
249:
245:
241:
236:
228:
227:
226:
224:
217:
215:
206:
200:Primary cause
199:
197:
195:
191:
187:
184:
180:
176:
172:
171:load on wheel
168:
164:
160:
156:
152:
148:
143:
141:
136:
134:
130:
126:
121:
117:
113:
109:
105:
101:
97:
93:
89:
85:
81:
77:
73:
66:
65:
60:
59:
54:
53:
48:
47:
42:
41:
37:
32:
19:
4415:Tire Society
4329:Tire changer
4324:Bead breaker
4294:Bicycle pump
4203:Tire balance
4182:
4113:Presta valve
4108:Dunlop valve
4050:Racing slick
4045:Tractor tire
4030:Tubular tire
4025:Bicycle tire
3955:Airless tire
3850:
3834:
3830:
3818:(in Russian)
3807:(in Russian)
3793:
3784:
3774:
3767:(in Russian)
3761:
3752:
3743:
3734:
3723:
3691:
3680:
3661:
3655:
3622:
3618:
3608:
3596:
3587:
3380:
3371:
3359:
3350:
3327:. Retrieved
3315:
3306:
3281:
3277:
3267:
3234:
3230:
3224:
3213:. Retrieved
3201:
3192:
3173:
3169:
3159:
3140:
3136:
3126:
3107:
3103:
3093:
3071:
3062:
3053:
3032:
3023:
2977:
2965:
2954:
2937:
2928:
2919:
2910:
2901:
2871:
2859:. Retrieved
2855:
2846:
2837:
2828:
2809:
2803:
2792:. Retrieved
2788:
2778:
2769:
2760:
2750:
2739:the original
2726:
2717:
2708:
2699:
2686:
2677:
2659:
2648:. Retrieved
2618:
2607:. Retrieved
2595:
2570:
2545:
2539:. Retrieved
2530:
2523:
2512:. Retrieved
2500:
2440:
2433:
2429:
2425:
2414:(Russia) or
2405:
2385:
2320:
2298:
2247:or railroad
2242:
2228:
2220:
2216:
2202:
2181:
2174:
2158:
2146:
2134:transmission
2131:
2083:
1928:The driving
1927:
1919:
1910:
1893:
1870:
1856:
1842:
1812:Large truck
1804:
1780:
1766:
1751:
1743:eco-marathon
1726:
1711:
1694:
1686:
1680:
1679:
1673:
1668:
1667:
1658:
1449:
1443:
1439:
1413:
1409:
1300:
1296:
1275:one can use
1242:
1037:
940:
932:
870:
849:
735:
730:
469:
464:normal force
437:
433:
429:
310:
297:
293:
289:
285:
274:
270:
252:
237:
233:
219:
211:
144:
137:
128:
124:
110:losses (see
80:rolling drag
79:
75:
71:
70:
63:
62:
57:
56:
51:
50:
45:
44:
39:
38:
4443:Plus sizing
4367:Waste tires
4319:Direct TPMS
4304:Tire mousse
4276:Maintenance
4251:Aquaplaning
4020:Tundra tire
4000:Paddle tire
3985:Knobby tire
3935:Radial tire
3284:: 974–983.
2412:cylindrical
2304:tires on a
2140:(including
1757:0.5 mm
1717:0.1 mm
1687:Description
846:Measurement
267:Definitions
179:rubber tire
104:non-elastic
4496:Categories
4448:Tire label
4344:Life cycle
4266:Tramlining
4193:Slip angle
4130:Attributes
4103:Valve stem
4075:Components
4060:Spare tire
3990:Large tire
3329:2021-04-19
3215:2021-04-19
2995:Gillespie
2861:7 February
2794:2017-08-05
2650:2007-08-11
2609:2017-07-11
2541:2007-10-09
2514:2021-04-19
2481:References
2469:Levitation
2358:In tires,
2351:increases.
2128:All wheels
214:hysteresis
175:hysteresis
108:hysteresis
4438:Tire code
4387:Flat tire
4377:Tire fire
4334:Tire iron
4243:Behaviors
4035:Lego tire
3970:Snow tire
3965:Rain tyre
3647:109914430
3562:
3538:
3522:this rule
3298:0306-2619
3259:199099736
3251:0954-4070
3086:talk page
2289:cornering
2273:rail cant
2107:Ω
2068:Ω
2004:Ω
1739:solar car
1158:0.0643988
898:θ
892:
860:SAE J2452
856:SAE J1269
840:it is not
125:slip loss
4481:Category
4088:Beadlock
3980:Bar grip
3779:bearing.
2667:Archived
2466:Magnetic
2446:See also
2283:but for
2192:adhesion
2177:traction
1736:Michelin
1734:Special
1498:, gives
776:diameter
194:concrete
133:friction
120:slippage
4382:Blowout
4362:Retread
3627:Bibcode
2416:tapered
2306:roadway
2265:Banking
2239:General
1896:newtons
1869:0.0385
1855:0.0100
1841:0.0062
1803:0.0045
1783:0.0050
1779:0.0022
1765:0.0019
1750:0.0010
1729:0.0025
1725:0.0010
1714:0.0015
1710:0.0010
1693:0.0003
1408:is the
462:is the
147:vehicle
3668:
3645:
3520:using
3420:where
3296:
3257:
3249:
2999:
2893:
2816:
2583:
2579:–442.
2462:Maglev
2253:banked
2138:brakes
2028:where
1930:torque
1883:0.3000
1873:0.0730
1859:0.0150
1845:0.0150
1831:0.0065
1821:0.0055
1816:tires
1814:(Semi)
1807:0.0080
1793:0.0050
1769:0.0065
1754:0.0024
1745:tires
1697:0.0004
1442:, not
1341:where
1194:where
1092:0.0048
989:where
921:radius
875:length
772:torque
508:
440:), and
353:where
319:
256:silica
248:moment
84:motion
4093:Tread
3960:Tweel
3922:Types
3914:Tires
3643:S2CID
3524:that
3255:S2CID
3018:data.
2946:(PDF)
2742:(PDF)
2735:(PDF)
2645:(PDF)
2604:(PDF)
2360:tread
2310:sound
2295:Sound
2285:roads
2275:of a
2249:train
2184:creep
2154:power
768:loads
630:just
183:steel
155:rails
151:train
112:below
100:rolls
96:wheel
94:, or
4083:Bead
3666:ISBN
3603:2017
3294:ISSN
3247:ISSN
3003:p117
2997:ISBN
2891:ISBN
2863:2012
2814:ISBN
2692:here
2581:ISBN
2363:out.
2277:rail
858:and
701:1000
638:2000
527:0.01
190:sand
92:tire
88:ball
3635:doi
3406:0.5
3320:doi
3286:doi
3282:157
3239:doi
3235:234
3206:doi
3178:doi
3145:doi
3112:doi
2577:441
2536:135
2505:doi
2408:Crr
1412:or
1299:or
1127:100
889:cos
881:of
438:CRF
432:or
159:bus
127:or
78:or
4498::
3702:^
3641:.
3633:.
3621:.
3617:.
3338:^
3318:.
3314:.
3292:.
3280:.
3276:.
3253:.
3245:.
3233:.
3204:.
3200:.
3174:50
3172:.
3168:.
3141:50
3139:.
3135:.
3108:50
3106:.
3102:.
3041:^
3008:^
2988:^
2882:^
2854:.
2787:.
2629:^
2553:^
2544:.
2503:.
2499:.
2488:^
2291:.
1871:to
1857:to
1843:to
1805:to
1781:to
1767:to
1752:to
1727:to
1712:to
1695:to
1674:rr
1651:.
1518:=
1098:18
842:.
770:,
258:.
216::
169:,
98:)
90:,
3906:e
3899:t
3892:v
3717:.
3674:.
3649:.
3637::
3629::
3623:2
3569:F
3565:F
3559:d
3553:2
3550:=
3545:N
3541:N
3535:d
3508:N
3488:F
3468:k
3448:N
3428:F
3402:N
3398:k
3395:=
3392:F
3332:.
3322::
3300:.
3288::
3261:.
3241::
3218:.
3208::
3186:.
3180::
3153:.
3147::
3120:.
3114::
3088:.
2948:.
2865:.
2822:.
2797:.
2694:.
2653:.
2612:.
2589:.
2517:.
2507::
2464:(
2370:.
2347:.
2103:/
2097:s
2093:V
2044:s
2040:V
2014:r
2010:R
1999:s
1995:V
1989:=
1986:T
1964:r
1960:R
1939:T
1741:/
1681:b
1669:C
1639:r
1617:r
1614:r
1610:C
1589:b
1567:r
1564:r
1560:C
1539:r
1534:r
1531:r
1527:C
1506:b
1486:b
1458:r
1444:R
1440:W
1426:N
1396:b
1374:r
1352:F
1327:r
1323:b
1320:N
1314:=
1311:F
1283:b
1260:r
1257:r
1253:C
1227:W
1205:D
1178:4
1171:2
1167:D
1163:W
1153:=
1147:4
1144:1
1139:)
1135:W
1131:/
1124:(
1118:2
1115:1
1110:)
1106:D
1102:/
1095:(
1089:=
1084:r
1081:r
1077:C
1054:r
1051:r
1047:C
1022:d
1000:z
975:d
971:/
967:z
962:=
957:r
954:r
950:C
907:1
904:=
901:)
895:(
871:b
824:r
821:r
817:C
794:r
791:r
787:C
752:r
749:r
745:C
731:g
715:r
712:r
708:C
704:g
679:r
676:r
672:C
649:r
646:r
642:C
615:r
612:r
608:C
585:r
582:r
578:C
555:r
552:r
548:C
524:=
519:r
516:r
512:C
485:r
482:r
478:C
450:N
436:(
414:r
411:r
407:C
384:R
364:F
341:N
336:r
333:r
329:C
325:=
322:F
64:R
58:r
52:F
46:W
40:R
20:)
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